Let p be a prime number. For example, p could be 2,3,5,7, etc. We define a field Fp consisting of the elements {0, 1, 2, . . . , p − 1} with operations +, −, ×, ÷ considered only up to remainder when wedividebyp. Forexample,inF5,2+4=6≡1,2−4=−2≡3,and2×4=8≡3. SinceF5, 4 × 3 = 12 ≡ 2 (you can check that the multiplication of 4 with any other element in F5 is never 2), we say that 2 ÷ 4 ≡ 3 in F5. Question #1: Consider F5. Compute a+b,a−b,a×b,a÷b for all a,b∈{0,1,2,3,4}.
Let p be a prime number. For example, p could be 2,3,5,7, etc. We define a field Fp consisting of the elements {0, 1, 2, . . . , p − 1} with operations +, −, ×, ÷ considered only up to remainder when wedividebyp. Forexample,inF5,2+4=6≡1,2−4=−2≡3,and2×4=8≡3. SinceF5, 4 × 3 = 12 ≡ 2 (you can check that the multiplication of 4 with any other element in F5 is never 2), we say that 2 ÷ 4 ≡ 3 in F5. Question #1: Consider F5. Compute a+b,a−b,a×b,a÷b for all a,b∈{0,1,2,3,4}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let p be a prime number. For example, p could be 2,3,5,7, etc. We define a field Fp consisting of the elements {0, 1, 2, . . . , p − 1} with operations +, −, ×, ÷ considered only up to remainder when wedividebyp. Forexample,inF5,2+4=6≡1,2−4=−2≡3,and2×4=8≡3. SinceF5, 4 × 3 = 12 ≡ 2 (you can check that the multiplication of 4 with any other element in F5 is never 2), we say that 2 ÷ 4 ≡ 3 in F5.
Question #1: Consider F5. Compute a+b,a−b,a×b,a÷b for all a,b∈{0,1,2,3,4}.
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